Welcome to our forum.
I don't see any problem with trying to persuade your wife to change her mind about the real-life sex thing. However, if she remains unpersuaded and still says no, you probably either have to abide by what she says, or start thinking about a divorce. As far as "hurting your relationship with T because of the no-sex thing," I would think that if you explained the situation to T, she would understand and support your position. Sure relationships need to grow, but that doesn't always mean sex, we all have platonic relationships that do just fine without sex.
I have not personally had any online romances, much less one that transitioned into an long-distance relationship. So I can't provide you with much advice about that. I think LDR's tend to be challenging, and need lots of communication while you're apart.
Sorry there are no easy answers that I know of. Hopefully you and your wife can continue to have conversations that clear things up and smooth over some of the roughness.
Have a look around on our site, and post your thoughts, questions, and concerns as they come to you.
Love means never having to say, "Put down that meat cleaver!"